(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 92123, 12951]*) (*NotebookOutlinePosition[ 92982, 12982]*) (* CellTagsIndexPosition[ 92938, 12978]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ Mathematica Problem Set 2 \ \>", "Title", CellFrame->True, TextAlignment->Center, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ Use Mathematica to solve the following problems: \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ A firm produces output Q using labor, L, and capital, K. 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.30952 .1102 L .34656 .10347 L .3836 .09787 L .42063 .09312 L .45767 .08903 L .49471 .08547 L .53175 .08233 L .56878 .07953 L .60582 .07702 L .64286 .07476 L .67989 .0727 L .71693 .07082 L .75397 .0691 L .79101 .06751 L .82804 .06603 L .86508 .06467 L .90212 .06339 L .93915 .0622 L .97619 .06108 L s P P p 1 0 0 r p .01 w .0873 .60332 m .09656 .55715 L .10582 .51953 L .12434 .46148 L .14286 .41838 L .16138 .38484 L .19841 .33551 L .23545 .30054 L .27249 .27418 L .30952 .25344 L .34656 .2366 L .3836 .2226 L .42063 .21073 L .45767 .20051 L .49471 .1916 L .53175 .18375 L .56878 .17676 L .60582 .17049 L .64286 .16483 L .67989 .15969 L .71693 .15499 L .75397 .15067 L .79101 .1467 L .82804 .14301 L .86508 .1396 L .90212 .13641 L .93915 .13343 L .97619 .13064 L s P P P % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->Infinity, ImageSize->{300, 185}, ImageMargins->{{100, Inherited}, {Inherited, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False]}, Open]], Cell["\<\ 4) Suppose the wage, W, equals 10 and the price of capital, r, equals .05, \ graph the equal-cost curves for total costs, TC, of $50, $100 and $200. \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ (TC = .05 K + 10 L) is the starting equation. When solved for K it yields \ (K = TC/.05 - 200 L). This will be plotted in blue along with TC at 100 \ (red) and TC at 200 (green). \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{Cell["\<\ Clear[TC1,TC2,TC3,L] TC1[L_] = 1000 - 200 L; TC2[L_] = 2000 - 200 L; TC3[L_] = 4000 - 200 L; Plot[{TC1[L],TC2[L],TC3[L]},{L,0,4000/200}, PlotRange->{0,4000}, PlotStyle->{{Blue,Thickness[0.01]}, {Red,Thickness[0.010]},{Green,Thickness[0.01]}}, AxesLabel->{\"Labor\",\"Capital\"}, PlotLabel->\"Equal Cost Lines 1, 2 & 3\"]; \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.047619 -1.51788e-17 0.000154508 [ [(0)] .02381 0 0 2 Msboxa [(5)] .2619 0 0 2 Msboxa [(10)] .5 0 0 2 Msboxa [(15)] .7381 0 0 2 Msboxa [(20)] .97619 0 0 2 Msboxa [(Labor)] 1.025 0 -1 0 Msboxa [(Equal Cost Lines 1, 2 & 3)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(500)] .01131 .07725 1 0 Msboxa [(1000)] .01131 .15451 1 0 Msboxa [(1500)] .01131 .23176 1 0 Msboxa [(2000)] .01131 .30902 1 0 Msboxa [(2500)] .01131 .38627 1 0 Msboxa [(3000)] .01131 .46353 1 0 Msboxa [(3500)] .01131 .54078 1 0 Msboxa [(4000)] .01131 .61803 1 0 Msboxa [(Capital)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .2619 0 m .2619 .00625 L s P [(5)] .2619 0 0 2 Mshowa p .002 w .5 0 m .5 .00625 L s P [(10)] .5 0 0 2 Mshowa p .002 w .7381 0 m .7381 .00625 L s P [(15)] .7381 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(20)] .97619 0 0 2 Mshowa p .001 w .07143 0 m .07143 .00375 L s P p .001 w .11905 0 m .11905 .00375 L s P p .001 w .16667 0 m .16667 .00375 L s P p .001 w .21429 0 m .21429 .00375 L s P p .001 w .30952 0 m .30952 .00375 L s P p .001 w .35714 0 m .35714 .00375 L s P p .001 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[(14)] .9127 0 0 2 Mshowa p .001 w .04921 0 m .04921 .00375 L s P p .001 w .0746 0 m .0746 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1254 0 m .1254 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .20159 0 m .20159 .00375 L s P p .001 w .22698 0 m .22698 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .30317 0 m .30317 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .35397 0 m .35397 .00375 L s P p .001 w .37937 0 m .37937 .00375 L s P p .001 w .43016 0 m .43016 .00375 L s P p .001 w .45556 0 m .45556 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .50635 0 m .50635 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .58254 0 m .58254 .00375 L s P p .001 w .60794 0 m .60794 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .68413 0 m .68413 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .73492 0 m .73492 .00375 L s P p .001 w .76032 0 m .76032 .00375 L s P p .001 w .81111 0 m .81111 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Msboxa [(200)] .65873 0 0 2 Msboxa [(250)] .81746 0 0 2 Msboxa [(300)] .97619 0 0 2 Msboxa [(Quantity)] 1.025 0 -1 0 Msboxa [(Average and Marginal Cost)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(0.2)] .01131 .12361 1 0 Msboxa [(0.4)] .01131 .24721 1 0 Msboxa [(0.6)] .01131 .37082 1 0 Msboxa [(0.8)] .01131 .49443 1 0 Msboxa [(1)] .01131 .61803 1 0 Msboxa [(Cost)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .18254 0 m .18254 .00625 L s P [(50)] .18254 0 0 2 Mshowa p .002 w .34127 0 m .34127 .00625 L s P [(100)] .34127 0 0 2 Mshowa p .002 w .5 0 m .5 .00625 L s P [(150)] .5 0 0 2 Mshowa p .002 w .65873 0 m .65873 .00625 L s P [(200)] .65873 0 0 2 Mshowa p .002 w .81746 0 m .81746 .00625 L s P [(250)] .81746 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(300)] .97619 0 0 2 Mshowa p .001 w .05556 0 m 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[(Average and Marginal Cost)] .5 .61803 0 -2 0 0 1 Mouter Mrotshowa p .002 w .02381 .12361 m .03006 .12361 L s P [(0.2)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(0.4)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(0.6)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(0.8)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(1)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P [(Cost)] .02381 .61803 0 -4 Mshowa p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p 0 0 1 r p .015 w .02381 .14551 m .06349 .14551 L .10317 .14551 L .14286 .14551 L .18254 .14551 L .22222 .14551 L .2619 .14551 L .30159 .14551 L .34127 .14551 L .38095 .14551 L .42063 .14551 L .46032 .14551 L .5 .14551 L .53968 .14551 L .57937 .14551 L .61905 .14551 L .65873 .14551 L .69841 .14551 L .7381 .14551 L .77778 .14551 L .81746 .14551 L .85714 .14551 L .89683 .14551 L .93651 .14551 L .97619 .14551 L s P P p 1 0 0 r p .01 w .02381 .14551 m .06349 .14551 L .10317 .14551 L .14286 .14551 L .18254 .14551 L .22222 .14551 L .2619 .14551 L .30159 .14551 L .34127 .14551 L .38095 .14551 L .42063 .14551 L .46032 .14551 L .5 .14551 L .53968 .14551 L .57937 .14551 L .61905 .14551 L .65873 .14551 L .69841 .14551 L .7381 .14551 L .77778 .14551 L .81746 .14551 L .85714 .14551 L .89683 .14551 L .93651 .14551 L .97619 .14551 L s P P P % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->Infinity, ImageSize->{300, 185}, ImageMargins->{{100, Inherited}, {Inherited, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False]}, Open]], Cell["\<\ 9) Suppose this is a monopoly firm facing the demand curve: P= 1 - .00093 Q where P is the price of its output. Graph the demand and marginal revenue, \ MR, curve for this firm. \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{Cell["\<\ Clear[P,MR,Q] P[Q_] = 1 - .00093 Q; MR[Q_] = 1 - .00093 (2 Q); Plot[{P[Q],MR[Q]},{Q,0,1/.00093}, PlotRange->{0,1}, PlotStyle->{{Blue,Thickness[0.01]}, {Red,Thickness[0.010]}}, AxesLabel->{\"Quantity\",\"Price\"}, PlotLabel->\" Demand and Marginal Revenue\"]; \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.000885714 0 0.618034 [ [(0)] .02381 0 0 2 Msboxa [(200)] .20095 0 0 2 Msboxa [(400)] .3781 0 0 2 Msboxa [(600)] .55524 0 0 2 Msboxa [(800)] .73238 0 0 2 Msboxa [(1000)] .90952 0 0 2 Msboxa [(Quantity)] 1.025 0 -1 0 Msboxa [( Demand and Marginal Revenue)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(0.2)] .01131 .12361 1 0 Msboxa [(0.4)] .01131 .24721 1 0 Msboxa [(0.6)] .01131 .37082 1 0 Msboxa [(0.8)] .01131 .49443 1 0 Msboxa [(1)] .01131 .61803 1 0 Msboxa [(Price)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .20095 0 m .20095 .00625 L s P [(200)] .20095 0 0 2 Mshowa p .002 w .3781 0 m .3781 .00625 L s P [(400)] .3781 0 0 2 Mshowa p .002 w .55524 0 m .55524 .00625 L s P [(600)] .55524 0 0 2 Mshowa p .002 w .73238 0 m .73238 .00625 L s P [(800)] .73238 0 0 2 Mshowa p .002 w .90952 0 m .90952 .00625 L s P [(1000)] .90952 0 0 2 Mshowa p .001 w .05924 0 m .05924 .00375 L s P p .001 w .09467 0 m .09467 .00375 L s P p .001 w .1301 0 m .1301 .00375 L s P p .001 w .16552 0 m .16552 .00375 L s P p .001 w .23638 0 m .23638 .00375 L s P p .001 w .27181 0 m .27181 .00375 L s P p .001 w .30724 0 m .30724 .00375 L s P p .001 w .34267 0 m .34267 .00375 L s P p .001 w .41352 0 m .41352 .00375 L s P p .001 w .44895 0 m .44895 .00375 L s P p .001 w .48438 0 m .48438 .00375 L s P p .001 w .51981 0 m .51981 .00375 L s P p .001 w .59067 0 m .59067 .00375 L s P p .001 w .6261 0 m .6261 .00375 L s P p .001 w .66152 0 m .66152 .00375 L s P p .001 w .69695 0 m .69695 .00375 L s P p .001 w .76781 0 m .76781 .00375 L s P p .001 w .80324 0 m .80324 .00375 L s P p .001 w .83867 0 m .83867 .00375 L s P p .001 w .8741 0 m .8741 .00375 L s P p .001 w .94495 0 m .94495 .00375 L s P p .001 w .98038 0 m .98038 .00375 L s P [(Quantity)] 1.025 0 -1 0 Mshowa p .002 w 0 0 m 1 0 L s P [( Demand and Marginal Revenue)] .5 .61803 0 -2 0 0 1 Mouter Mrotshowa p .002 w .02381 .12361 m .03006 .12361 L s P [(0.2)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(0.4)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(0.6)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(0.8)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(1)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P [(Price)] .02381 .61803 0 -4 Mshowa p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p 0 0 1 r p .01 w .02381 .61803 m .06349 .59228 L .10317 .56653 L .14286 .54078 L .18254 .51503 L .22222 .48928 L .2619 .46353 L .30159 .43777 L .34127 .41202 L .38095 .38627 L .42063 .36052 L .46032 .33477 L .5 .30902 L .53968 .28327 L .57937 .25751 L .61905 .23176 L .65873 .20601 L .69841 .18026 L .7381 .15451 L .77778 .12876 L .81746 .10301 L .85714 .07725 L .89683 .0515 L .93651 .02575 L .97619 0 L s P P p 1 0 0 r p .01 w .02381 .61803 m .06349 .56653 L .10317 .51503 L .14286 .46353 L .18254 .41202 L .22222 .36052 L .2619 .30902 L .30159 .25751 L .34127 .20601 L .38095 .15451 L .42063 .10301 L .46032 .0515 L .5 0 L s s s s s s s s s s s s s P P P % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->Infinity, ImageSize->{300, 185}, ImageMargins->{{100, Inherited}, {Inherited, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False]}, Open]], Cell["\<\ 10) Add the marginal cost and average cost curves to your diagram in question \ 9 and determine the profit maximizing output for the firm. What are the \ monopoly profits? \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{Cell["\<\ Clear[P,MR,Q] P[Q_] = 1 - .00093 Q; MR[Q_] = 1 - .00093 (2 Q); Plot[{P[Q],MR[Q],MC[Q],AC[Q]},{Q,0,1/.00093}, PlotRange->{0,1}, PlotStyle->{{Blue,Thickness[0.01]}, {Red,Thickness[0.010]},{Green,Thickness[0.015]}, \t{Blue,Thickness[0.01]}}, AxesLabel->{\"Quantity\",\"Cost\"}, PlotLabel->\"The Monopoly Firm\"]; \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.000885714 0 0.618034 [ [(0)] .02381 0 0 2 Msboxa [(200)] .20095 0 0 2 Msboxa [(400)] .3781 0 0 2 Msboxa [(600)] .55524 0 0 2 Msboxa [(800)] .73238 0 0 2 Msboxa [(1000)] .90952 0 0 2 Msboxa [(Quantity)] 1.025 0 -1 0 Msboxa [(The Monopoly Firm)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(0.2)] .01131 .12361 1 0 Msboxa [(0.4)] .01131 .24721 1 0 Msboxa [(0.6)] .01131 .37082 1 0 Msboxa [(0.8)] .01131 .49443 1 0 Msboxa [(1)] .01131 .61803 1 0 Msboxa [(Cost)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .20095 0 m .20095 .00625 L s P [(200)] .20095 0 0 2 Mshowa p .002 w .3781 0 m .3781 .00625 L s P [(400)] .3781 0 0 2 Mshowa p .002 w .55524 0 m .55524 .00625 L s P [(600)] .55524 0 0 2 Mshowa p .002 w .73238 0 m .73238 .00625 L s P [(800)] .73238 0 0 2 Mshowa p .002 w .90952 0 m .90952 .00625 L s P [(1000)] .90952 0 0 2 Mshowa p .001 w .05924 0 m .05924 .00375 L s P p .001 w .09467 0 m .09467 .00375 L s P p .001 w .1301 0 m .1301 .00375 L s P p .001 w .16552 0 m .16552 .00375 L s P p .001 w .23638 0 m .23638 .00375 L s P p .001 w .27181 0 m .27181 .00375 L s P p .001 w .30724 0 m .30724 .00375 L s P p .001 w .34267 0 m .34267 .00375 L s P p .001 w .41352 0 m .41352 .00375 L s P p .001 w .44895 0 m .44895 .00375 L s P p .001 w .48438 0 m .48438 .00375 L s P p .001 w .51981 0 m .51981 .00375 L s P p .001 w .59067 0 m .59067 .00375 L s P p .001 w .6261 0 m .6261 .00375 L s P p .001 w .66152 0 m .66152 .00375 L s P p .001 w .69695 0 m .69695 .00375 L s P p .001 w .76781 0 m .76781 .00375 L s P p .001 w .80324 0 m .80324 .00375 L s P p .001 w .83867 0 m .83867 .00375 L s P p .001 w .8741 0 m .8741 .00375 L s P p .001 w .94495 0 m .94495 .00375 L s P p .001 w .98038 0 m .98038 .00375 L s P [(Quantity)] 1.025 0 -1 0 Mshowa p .002 w 0 0 m 1 0 L s P [(The Monopoly Firm)] .5 .61803 0 -2 0 0 1 Mouter Mrotshowa p .002 w .02381 .12361 m .03006 .12361 L s P [(0.2)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(0.4)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(0.6)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(0.8)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(1)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P [(Cost)] .02381 .61803 0 -4 Mshowa p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p 0 0 1 r p .01 w .02381 .61803 m .06349 .59228 L .10317 .56653 L .14286 .54078 L .18254 .51503 L .22222 .48928 L .2619 .46353 L .30159 .43777 L .34127 .41202 L .38095 .38627 L .42063 .36052 L .46032 .33477 L .5 .30902 L .53968 .28327 L .57937 .25751 L .61905 .23176 L .65873 .20601 L .69841 .18026 L .7381 .15451 L .77778 .12876 L .81746 .10301 L .85714 .07725 L .89683 .0515 L .93651 .02575 L .97619 0 L s P P p 1 0 0 r p .01 w .02381 .61803 m .06349 .56653 L .10317 .51503 L .14286 .46353 L .18254 .41202 L .22222 .36052 L .2619 .30902 L .30159 .25751 L .34127 .20601 L .38095 .15451 L .42063 .10301 L .46032 .0515 L .5 0 L s s s s s s s s s s s s s P P p 0 1 0 r p .015 w .02381 .14551 m .06349 .14551 L .10317 .14551 L .14286 .14551 L .18254 .14551 L .22222 .14551 L .2619 .14551 L .30159 .14551 L .34127 .14551 L .38095 .14551 L .42063 .14551 L .46032 .14551 L .5 .14551 L .53968 .14551 L .57937 .14551 L .61905 .14551 L .65873 .14551 L .69841 .14551 L .7381 .14551 L .77778 .14551 L .81746 .14551 L .85714 .14551 L .89683 .14551 L .93651 .14551 L .97619 .14551 L s P P p 0 0 1 r p .01 w .02381 .14551 m .06349 .14551 L .10317 .14551 L .14286 .14551 L .18254 .14551 L .22222 .14551 L .2619 .14551 L .30159 .14551 L .34127 .14551 L .38095 .14551 L .42063 .14551 L .46032 .14551 L .5 .14551 L .53968 .14551 L .57937 .14551 L .61905 .14551 L .65873 .14551 L .69841 .14551 L .7381 .14551 L .77778 .14551 L .81746 .14551 L .85714 .14551 L .89683 .14551 L .93651 .14551 L .97619 .14551 L s P P P % End of Graphics MathPictureEnd \ \>"], "Graphics", PageWidth->Infinity, ImageSize->{300, 185}, ImageMargins->{{100, Inherited}, {Inherited, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False]}, Open]], Cell[CellGroupData[{Cell["\<\ Solve[ MC[Q] == MR[Q],Q] \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[OutputFormData["\<\ {{Q -> 411.0559139784947}} \ \>", "\<\ {{Q -> 411.056}} \ \>"], "Output", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}]}, Open]], Cell[CellGroupData[{Cell["\<\ (P[411.056] - AC[411.056]) * 411.056 \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[OutputFormData["\<\ 157.13927690752 \ \>", "\<\ 157.139 \ \>"], "Output", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}]}, Open]], Cell["\<\ The profit maximizing output is 411.056 and the monopoly profits are 157.139. \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ 11.) Determine the price and output if this were a competitive industry. \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{Cell["\<\ Solve[MC[Q] == P[Q],Q] \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[OutputFormData["\<\ {{Q -> 822.111827956989}} \ \>", "\<\ {{Q -> 822.112}} \ \>"], "Output", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}]}, Open]], Cell[CellGroupData[{Cell["\<\ P[822.112] \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[OutputFormData["\<\ 0.23543584 \ \>", "\<\ 0.235436 \ \>"], "Output", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}]}, Open]], Cell["\<\ The price would be .235436 and the quantity would be822.112 if this were a \ competitive industry. \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ 12.) Determine the deadweight loss of this monopoly. \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{Cell["\<\ (822.112 - 411.056)*(P[411.056] - .235436)/2 \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[OutputFormData["\<\ 78.56963845376001 \ \>", "\<\ 78.5696 \ \>"], "Output", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}]}, Open]] }, FrontEndVersion->"4.1 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, WindowToolbars->{}, CellGrouping->Manual, WindowSize->{499, 599}, WindowMargins->{{73, Automatic}, {Automatic, 0}}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, -1}}, ShowCellLabel->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False} ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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